1. Computer and Network Security
CSEN 1001
Computer and Network Security
Amr El Mougy
Alaa Gohar

2. Lecture (2)
Cryptographic Tools

3. Early History
Egypt (Old Kingdom), ca. 1900BC. Use of non-standard hieroglyphs (probably not a serious attempt at secret communication)
Mesopotamia, ca. 1500BC. Encrypted recipe for pottery glaze on clay tablet
Hebrew, ca. 500BC. Monoalphabetic substitution cipher used by scholars

4. Not so Early History
800AD. Early description of frequency analysis for breaking substitution ciphers (credited to Arab mathematician Al- Kindi, 801–873). Works about cryptanalysis of single- and polyalphabetic ciphers
Ahmad al-Qalqashandi 1355–1418 List of ciphers in his encyclopedia contains a cipher with multiple substitutions for each letter; frequency tables for letters to aid cryptanalysis
1467: Leon Battista Alberti (“father of Western cryptology”) describes the polyalphabetic cipher

5. Recent History
WWII heavy use of rotor machines for complex polyalphabetic substitution ciphers
The “Enigma” machine:

6. Recent History
The time of WWII brought massive advances in cryptography as well as cryptanalysis
In the 20th century, mathematical cryptography was developed
Works by Claude Shannon. Any theoretically unbreakable cipher must have keys which are at least as long as the plaintext and used only once (one-time pad)
Publication of the Data Encryption Standard in 1970
1976 Ground-breaking paper: Whitfield Diffie and Martin Hellman. “New Directions in Cryptography” solves key exchange problem and sparks development of asymmetric key algorithms

7. Classical Substitution Ciphers
Where letters of plaintext are replaced by other letters or by numbers or symbols
Or if plaintext is viewed as a sequence of bits, then substitution involves replacing plaintext bit patterns with ciphertext bit patterns

8. Caesar Cipher
Earliest known substitution cipher (invented by Julius Caesar)
First attested use in military affairs
Replaces each letter by 3rd letter down in the alphabet. Example:
Meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB
Can define transformation as:
a b c d e f g h i j k l m n o p q r s t u v w x y z
D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
Mathematically give each letter a number
a b c d e f g h i j k l m n o p q r s t u v w x y z
Then have Caesar cipher as:
c = E(p) = (p + k) mod (26)
p = D(c) = (c – k) mod (26)

9. Breaking Caesar Cipher
Only have 26 possible ciphers
A maps to A,B,..Z
Could simply try each in turn
a brute force search
Given ciphertext, just try all shifts of letters
Do need to recognize when have plaintext
Compression reduces chance of breaking

10. Monoalphabetic Cipher
Rather than just shifting the alphabet, shuffle (jumble) the letters arbitrarily
Each plaintext letter maps to a different random ciphertext letter
Hence key is 26 letters long
Plain: abcdefghijklmnopqrstuvwxyz
Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN
Plaintext: ifwewishtoreplaceletters
Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA
Now have a total of 26! = 4 x 1026 keys
With so many keys, might think is secure
But would be !!!WRONG!!!

11. Breaking the Monoalphabetic Cipher
Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

12. Breaking the Monoalphabetic Cipher
Human languages are redundant, eg “secrty s awsm"
letters are not equally commonly used
In English E is by far the most common letter
followed by T,R,N,I,O,A,S
Other letters like Z,J,K,Q,X are fairly rare
Have tables of single, double & triple letter frequencies for various languages

13. Breaking the Monoalphabetic Cipher
Key concept - monoalphabetic substitution ciphers do not change relative letter frequencies
Discovered by Arabian scientists in 9th century
Calculate letter frequencies for ciphertext
Compare counts/plots against known values
If Caesar cipher look for common peaks/troughs
peaks at: A-E-I triple, NO pair, RST triple
troughs at: JK, X-Z
For monoalphabetic must identify each letter
tables of common double/triple letters help

14. Breaking the Monoalphabetic Cipher
Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
Count relative letter frequencies
Guess P & Z are e and t
Guess ZW is “th” and hence ZWP is “the”. Frequency of two-letter combinations is known as digrams
Proceeding with trial and error finally get:
it was disclosed yesterday that several informal but
direct contacts have been made with political
representatives of the viet cong in moscow

15. Polyalphabetic Cipher
Improve security using multiple cipher alphabets
Make cryptanalysis harder with more alphabets to guess and flatter frequency distribution
Use a key to select which alphabet is used for each letter of the message
Use each alphabet in turn
Repeat from start after end of key is reached

16. Vigenère Cipher Simplest polyalphabetic substitution cipher
Effectively multiple Caesar ciphers
Key is multiple letters long K = k1 k2 ... kd , ith letter specifies ith alphabet to use
Use each alphabet in turn
Repeat from start after d letters in message
Decryption simply works in reverse
Write the plaintext out. Write the keyword repeated above it
Use each key letter as a Caesar cipher key. Encrypt the corresponding plaintext letter
eg using keyword deceptive
key:
plaintext:
ciphertext: d e c p t i v w a r s o y u l f Z I C V T W Q N G R A H Y L M J

17. Plaintext
Key

18. Breaking the Vigenère Cipher
Have multiple ciphertext letters for each plaintext letter
Hence letter frequencies are obscured, but not totally lost
Start with letter frequencies
see if look like monoalphabetic or not
If not, then need to determine number of alphabets, since then can attach each
Kasiski method developed by Babbage/Kasiski is a way of breaking Vigenere
Repetitions in ciphertext give clues to period, so find same plaintext an exact period apart which results in the same ciphertext
Of course, could also be random fluke
eg repeated “VTW” in previous example suggests size of 3 or 9
Then attack each monoalphabetic cipher individually using same techniques as before

19. One-time Pad
A random key as long as the message is used to encrypt and decrypt a single message
The key is then discarded, never to be used again
The output bears no statistical relationship to the plaintext
Given any plaintext of equal length to the ciphertext, there is a key that produces that plaintext. Therefore, if you did an exhaustive search of all possible keys, you would end up with many legible plaintexts, with no way of knowing which was the intended plaintext
ciphertext: ANKYODKYUREPFJBYOJDSPLREYIUNOFDOIUERFPLUYTS
key: pxlmvmsydofuyrvzwc tnlebnecvgdupahfzzlmnyih
plaintext: mr mustard with the candlestick in the hall
key: mfugpmiydgaxgoufhklllmhsqdqogtewbqfgyovuhwt
plaintext: miss scarlet with the knife in the library
Large number of keys need to be used. Key distribution is a big problem

20. Transposition Ciphers
Now consider classical transposition or permutation ciphers
These hide the message by rearranging the letter order without altering the actual letters used
Can recognise these since have the same frequency distribution as the original text
Simplest transposition cipher is the Rail Fence Cipher
Write message letters out diagonally over a number of rows
Then read off cipher row by row
eg. write message out as:
m e m a t r h t g p r y
e t e f e t e o a a t
Giving ciphertext
MEMATRHTGPRYETEFETEOAAT

21. Row Transposition Ciphers
A more complex transposition
Write letters of message out in rows over a specified number of columns, then reorder the columns according to some key before reading off the rows
Key:
Plaintext:
Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ
Ciphers using substitutions or transpositions are not secure because of language characteristics
Hence consider using several ciphers in succession to make harder, but:
two substitutions make a more complex substitution
two transpositions make more complex transposition
but a substitution followed by a transposition makes a new much harder cipher 4 3 1 2 5 6 7 a t c k P o s n e d u i l w m x y Z

22. Rotor Machines
Before modern ciphers, rotor machines were most common complex ciphers in use
Widely used in WW2
German Enigma, Allied Hagelin, Japanese Purple
Implemented a very complex, varying substitution cipher
Used a series of cylinders, each giving one substitution, which rotated and changed after each letter was encrypted
With 3 cylinders have 263=17576 alphabets

23. Rotor Machines

24. Note
The material in this lecture can be found in Chapter 2, Cryptography and network security.